Module 3, Part 2 of 2

The illusion of safety

The holding whose number never falls is losing you money every year. The holding that falls one year in four is the one that gets you there. Part 1 explained why movement is expensive; this part is about what people do in response to it, which is usually worse than the movement was.

Time
About 45 minutes
Level
High school
You need first
Part 1, including the seven problems.
By the end of Part 2
You can say which kind of risk a holding carries, what mixing does, and why selling after a fall is a plan that loses money when executed perfectly.
Part 1 Averages, and the order things happen in. Part 2

Guess before you read on

Money sitting in an account that pays nothing

Inflation runs at 3% a year. The balance never changes and never falls. How many years until that money buys half what it buys today?

Two things are called risk

One is how much the number jumps around. The other is the chance of not having what you need when you need it. They are not the same, and for long-term money they point in opposite directions.

Cash scores perfectly on the first. The balance never falls, no statement ever brings bad news, and the loss is total over a working lifetime. A broad stock holding scores badly on the first and is the one that gets people to retirement.

Cash does not fall. It just buys less. That is not a smaller version of a loss, it is a loss that never shows up anywhere you would look for one. Nothing on the statement changes on the day it happens, because it happens on every day.

What cash actually does

The dashed line is the balance on your statement. The solid line is what that balance buys, measured in today's money.

Raise what the account pays until the two lines meet. At that rate your cash is just about holding its value. Now go and look up what your own account actually pays.

Buying power lost

What the statement says What it buys
Balance at the end
What that buys today
Halves in

What mixing buys you

Two holdings that do not move together can be blended into something that moves less than either of them, without giving up any of the average return. The blended average is the weighted average of the two, exactly. The blended movement is less. Getting less of one thing and none less of the other is as close to free as this subject gets.

The lever that matters is the last one. It sets how closely the two move together, and at perfect lockstep mixing buys nothing at all.

Push the last slider to the far right and the benefit disappears. Two holdings that move identically are one holding.

What these two holdings are. The first averages 7% a year with an 18% swing, the second 3% with a 6% swing. Those are round numbers, picked because they behave roughly like a broad stock index and a bond holding. Nobody measured them off a real market; they are here to teach with, and no real pair of investments holds a fixed relationship for thirty years the way these two do. Each run is also nudged so its average lands exactly on the stated figure, which a real thirty year stretch would never do. That is what keeps this demonstration about the mixing. Otherwise you would mostly be watching which holding got the luckier draw.
What the mixing saved

Higher return, moves more Lower return, moves less The blend
Blend moves
Weighted average of the two
Blend's average return
What it actually earned. The blend compounded at and ended at , against for the first holding alone and for the second. That is . Splitting your money in half does not split the compound return in half. The blend moves around less, and movement is what eats compound return. Do not read that as a guarantee: any one run can come out differently, so this line reports the run sitting in front of you and leaves the rule-making to you.

The most expensive thing people do

A fall you hold through is a movement in a number. A fall you sell into is a loss, because you have turned a price into a realized amount and then been absent for whatever came next.

Below, one investor holds through everything. The other sells to cash after any year worse than the trigger, waits, and returns. Try several market numbers and count how often getting out helped.

This models an unusually well-organized panic. Our investor sells at the start of the next year, well after the bottom. They buy back on a fixed schedule, without waiting until it feels safe again. And they pay no tax and no trading costs. Every one of those four things goes worse in a real panic.

What getting out cost

Held through everything Got out after bad years
Held through
Got out
Sat in cash
Times it sold: . Cash is assumed to earn 1% a year while sitting out. The plan is not "sell at the top and buy at the bottom", which nobody can do. It is the plan people actually follow: sell after it has already fallen, return after it has already recovered.

Seven problems

Estimate first, then check. An estimate within 25% counts.

Four situations you have not seen

Different setups from the ones above. Each turns on telling the two kinds of risk apart.

Write it down

Answers stay on this device. Nothing is graded and nothing is sent anywhere.

1. Where the money is

Think of money you or your family hold somewhere. Which of the two risks is it exposed to: the one where the number moves, or the one where the number holds still and buys less? Is that the right choice given when the money is needed?

2. Decide it today

Write down what you will do the next time something you own drops sharply in value. Do it today, while nothing is dropping. That is the exercise. When the fall comes you will not be in any state to think it through, and a rule you wrote calmly is the only thing you will have to hold on to.

3. The limit that matters to you

Read the fourth worked answer below, which lists what these models leave out. Which of those would matter most in your own situation?

Check yourself

Answer each one before revealing ours. If you read our answer first you will agree with it, which tells you nothing.

1. Two meanings of risk

Explain, without using the word "volatility", why cash and a stock index are each the riskier of the two depending on the question asked.

2. Why mixing works

Say why blending two holdings can reduce movement without reducing the average, and name the condition it depends on.

3. Sell low, buy high

Explain why "sell when it falls, buy back when it recovers" loses money even for someone who executes it perfectly.

4. Break the model

Name something these three panels leave out that would change what you should actually do.

Save or hand in your answers

This writes out everything saved on this device for Module 3, both parts: your guesses, every problem you attempted with the answer beside it, and all your written answers.

Everything here is read out of this browser and written into a file on your own machine. Nothing is uploaded, because there is no server to upload it to. Clearing removes Module 3's answers only.

Next: Module 4, managing risk

This module was about the risk you take on purpose, because it pays. The next one is about the risk you would pay to be rid of. They are opposite decisions and people routinely get them the wrong way round: cautious with the money that should be growing, and uninsured against the thing that would actually ruin them. It is also where the sentence above about cash gets its exception.

Start Module 4